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CS344: Introduction to Artificial
Intelligence
(associated lab: CS386)
Pushpak Bhattacharyya
CSE Dept.,
IIT Bombay
Lecture–1: Introduction
Persons involved
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Faculty instructor: Dr. Pushpak Bhattacharyya
(www.cse.iitb.ac.in/~pb)
TAs: Prashanth, Debraj, Ashutosh, Nirdesh, Raunak,
Gourab {pkamle, debraj, ashu, nirdesh, rpilani,
roygourab}@cse
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Course home page
 www.cse.iitb.ac.in/~cs344-2010 (will be up)
Venue: SIT Building: SIC301
1 hour lectures 3 times a week: Mon-11.30, Tue8.30, Thu-9.30 (slot 4)
Associated Lab: CS386- Monday 2-5 PM
Perspective
Disciplines which form the core of AI- inner circle
Fields which draw from these disciplines- outer circle.
Robotics
NLP
Expert
Systems
Search,
Reasoning,
Learning
Planning
Computer
Vision
Topics to be covered (1/2)
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Search
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Logic
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General Graph Search, A*
Iterative Deepening, α-β pruning, probabilistic
methods
Formal System
Propositional Calculus, Predicate Calculus, Fuzzy
Logic
Knowledge Representation
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Predicate calculus, Semantic Net, Frame
Script, Conceptual Dependency, Uncertainty
Topics to be covered (2/2)
Neural Networks: Perceptrons, Back Propagation, Self
Organization
 Statistical Methods
 Markov Processes and Random Fields
 Computer Vision, NLP, Machine Learning
 Planning: Robotic Systems
=================================(if possible)
 Anthropomorphic Computing: Computational
Humour, Computational Music
 IR and AI
 Semantic Web and Agents
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Resources
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Main Text:
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Other Main References:
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Principles of AI - Nilsson
AI - Rich & Knight
Knowledge Based Systems – Mark Stefik
Journals
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Artificial Intelligence: A Modern Approach by Russell & Norvik,
Pearson, 2003.
AI, AI Magazine, IEEE Expert,
Area Specific Journals e.g, Computational Linguistics
Conferences
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IJCAI, AAAI
Foundational Points
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Church Turing Hypothesis
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Anything that is computable is computable
by a Turing Machine
Conversely, the set of functions computed
by a Turing Machine is the set of ALL and
ONLY computable functions
Turing Machine
Finite State Head (CPU)
Infinite Tape (Memory)
Foundational Points
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(contd)
Physical Symbol System Hypothesis
(Newel and Simon)
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For Intelligence to emerge it is enough to
manipulate symbols
Foundational Points
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(contd)
Society of Mind (Marvin Minsky)
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Intelligence emerges from the interaction
of very simple information processing units
Whole is larger than the sum of parts!
Foundational Points
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(contd)
Limits to computability
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Halting problem: It is impossible to
construct a Universal Turing Machine that
given any given pair <M, I> of Turing
Machine M and input I, will decide if M
halts on I
What this has to do with intelligent
computation? Think!
Foundational Points
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(contd)
Limits to Automation
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Godel Theorem: A “sufficiently powerful”
formal system cannot be BOTH complete
and consistent
“Sufficiently powerful”: at least as powerful
as to be able to capture Peano’s Arithmetic
Sets limits to automation of reasoning
Foundational Points
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(contd)
Limits in terms of time and Space
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NP-complete and NP-hard problems: Time
for computation becomes extremely large
as the length of input increases
PSPACE complete: Space requirement
becomes extremely large
Sets limits in terms of resources
Two broad divisions of
Theoretical CS
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Theory A
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Algorithms and Complexity
Theory B
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Formal Systems and Logic
AI as the forcing function
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Time sharing system in OS
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Machine giving the illusion of attending
simultaneously with several people
Compilers
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Raising the level of the machine for better
man machine interface
Arose from Natural Language Processing
(NLP)
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NLP in turn called the forcing function for AI
Allied Disciplines
Philosophy
Maths
Economics
Knowledge Rep., Logic, Foundation of
AI (is AI possible?)
Search, Analysis of search algos, logic
Psychology
Expert Systems, Decision Theory,
Principles of Rational Behavior
Behavioristic insights into AI programs
Brain Science
Learning, Neural Nets
Physics
Learning, Information Theory & AI,
Entropy, Robotics
Computer Sc. & Engg. Systems for AI
Grading
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(i) Exams
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(ii) Study
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Midsem
Endsem
Class test
Seminar (in group)
(iii) Work
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Lab Assignments (cs386; in group)
Fuzzy Logic
Fuzzy Logic tries to capture the
human ability of reasoning with
imprecise information
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Models Human Reasoning
Works with imprecise statements such as:
In a process control situation, “If the
temperature is moderate and the pressure is
high, then turn the knob slightly right”
The rules have “Linguistic Variables”, typically
adjectives qualified by adverbs (adverbs are
hedges).
Underlying Theory: Theory of
Fuzzy Sets
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Intimate connection between logic and set theory.
Given any set ‘S’ and an element ‘e’, there is a very
natural predicate, μs(e) called as the belongingness
predicate.
The predicate is such that,
μs(e) = 1,
iff e ∈ S
= 0,
otherwise
For example, S = {1, 2, 3, 4}, μs(1) = 1 and μs(5) =
0
A predicate P(x) also defines a set naturally.
S = {x | P(x) is true}
For example, even(x) defines S = {x | x is even}
Fuzzy Set Theory (contd.)
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Fuzzy set theory starts by questioning the
fundamental assumptions of set theory viz., the
belongingness predicate, μ, value is 0 or 1.
Instead in Fuzzy theory it is assumed that,
μs(e) = [0, 1]
Fuzzy set theory is a generalization of classical set
theory also called Crisp Set Theory.
In real life belongingness is a fuzzy concept.
Example: Let, T = set of “tall” people
μT (Ram) = 1.0
μT (Shyam) = 0.2
Shyam belongs to T with degree 0.2.
Linguistic Variables
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Fuzzy sets are named
by Linguistic Variables
(typically adjectives). μtall(h)
Underlying the LV is a
numerical quantity
1
E.g. For ‘tall’ (LV),
‘height’ is numerical
quantity.
Profile of a LV is the
plot shown in the figure
0
shown alongside.
0.4
4.5
1
2
3
4
height h
5
6
Example Profiles
μpoor(w)
μrich(w)
wealth w
wealth w
Example Profiles
μA (x)
μA (x)
x
Profile representing
moderate (e.g. moderately rich)
x
Profile representing
extreme
Concept of Hedge
Hedge is an intensifier
 Example:
LV = tall, LV1 = very
tall, LV2 = somewhat
tall
 ‘very’ operation:
μvery tall(x) = μ2tall(x)
 ‘somewhat’ operation:
μsomewhat tall(x) = √(μtall(x))
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somewhat tall
tall
1
μtall(h)
0
very tall
h
Representation of Fuzzy sets
Let U = {x1,x2,…..,xn}
|U| = n
The various sets composed of elements from U are presented
as points on and inside the n-dimensional hypercube. The crisp
μA(x1)=0.3
sets are the corners of the hypercube.
μA(x2)=0.4
(0,1)
U={x1,x2}
(1,1)
x2
(x1,x2)
A(0.3,0.4)
x2
(1,0)
(0,0)
Φ
x1
x1
A fuzzy set A is represented by a point in the n-dimensional
space as the point {μA(x1), μA(x2),……μA(xn)}
Degree of fuzziness
The centre of the hypercube is the “most
fuzzy” set. Fuzziness decreases as one nears
the corners
Measure of fuzziness
Called the entropy of a fuzzy set
Fuzzy set
Farthest corner
E ( S )  d ( S , nearest ) / d ( S , farthest)
Entropy
Nearest corner
(0,1)
(1,1)
x2
(0.5,0.5)
A
d(A, nearest)
(0,0)
(1,0)
x1
d(A, farthest)
Definition
Distance between two fuzzy sets
n
d ( S1 , S 2 )   |  s1 ( xi )  s2 ( xi ) |
i 1
L1 - norm
Let C = fuzzy set represented by the centre point
d(c,nearest) = |0.5-1.0| + |0.5 – 0.0|
=1
= d(C,farthest)
=> E(C) = 1
Definition
Cardinality of a fuzzy set
n
m( s )   s ( xi ) [generalization of cardinality of
i 1
classical sets]
Union, Intersection, complementation, subset hood
 s s ( x)  max[  s ( x),  s ( x)]x U
1
2
1
2
 s s ( x)  min[  s ( x),  s ( x)]x U
1
2
 s ( x)  1   s ( x)
c
1
2
Note on definition by extension and intension
S1 = {xi|xi mod 2 = 0 } – Intension
S2 = {0,2,4,6,8,10,………..} – extension
How to define subset hood?